‘‘Fractional statistics’’ in arbitrary dimensions: A generalization of the Pauli principle

Abstract

The concept of ‘‘fractional statistics’’ is reformulated as a generalization of the Pauli exclusion principle, and a definition independent of the dimension of space is obtained. When applied to the vortexlike quasiparticles of the fractional quantum Hall effect, it gives the same result as that based on the braid-group. It is also used to classify spinons in gapless spin-1/2 antiferromagnetic chains as semions. An extensive one-particle Hilbert-space dimension is essential, limiting fractional statistics of this type to topological excitations confined to the interior of condensed matter. The new definition does not apply to ‘‘anyon gas’’ models as currently formulated: A possible resolution of this difficulty is proposed.